- #1

- 4

- 0

V(x)=

\begin{cases}

\infty,\quad x<0\\

0,\quad 0<x<a\\

V_o,\quad x>a.

\end{cases}

$$

I solved the time-independent Schrodinger equation for each region and after applying the continuity conditions of ##\Psi## and its derivative I ended up with:

$$ \tan(k_1a)=-\frac{k_1}{k_2},$$ where ##k_1=\sqrt{\frac{2mE}{\hbar^2}}## and ##k_2=\sqrt{\frac{2m(V_o-E)}{\hbar^2}}##.

I'm aware of the fact that solutions can only be calculated graphically, but what's the relation between the value of ##V_o## and the bound states? What if I want to find the acceptable values of ##V_o## for the bound states to be ##1,2,3,\dots## or none?